Pandemic preparedness and new model developments for airborne diseases transmitting via aerosols

Currently most computational models for airborne disease transmission in epidemics and pandemics are based on the Susceptible-Infected-Recovered, SIR, family of models. Although these models are suitable for describing diseases transmitting by direct contact, e.g., face-to-face coughing, they are less suitable for diseases transmitted by aerosols. In this study a general mathematical formulation for aerosol and direct transmission of an airborne infective agent is described. The formulation utilizes a multivariate population balance equation, PBE, framework that considers not just infected individuals but also infected indoor spaces. These PBEs are significantly more complex than SIR models and require simplifications to reduced models suitable for computational simulations. In this study two levels of reduced models are presented including univariate PBEs and compartment population level descriptions. It is shown how the SIR model can be extracted but also how the simplest possible aerosol SIR model, A-SIR, can be determined. The SIR and A-SIR models are compared for different scenarios and are shown to present significantly different dynamics and outcomes. Finally, the PBE approach appears to avoid many of the shortcomings of the SIR models noted in the literature and enables integration with other modeling approaches.